An experimental trial produces random variables X 1 and X 2 with correlation r E X 1 X 2 To estimate r, we perform n independent trials and form the estimate where X 1 (i) and X 2 (i) are samples of X 1 and X 2 on trial i Show that if Var X 1 X 2 is finite, then is an unbiased, consistent sequence ...

This problem is really very simple If we let Y X 1 X ...

An experimental trial produces random variables X 1 and X 2 with correlation r = E[X 1

Question:

An experimental trial produces random variables X₁and X₂with correlation r = E[X₁X₂]. To estimate r, we perform n independent trials and form the estimate

Σ: Π. ΣΧ 1) Χ. (i), Τη Σ i=1

where X₁(i) and X₂(i) are samples of X₁ and X₂ on trial i. Show that if Var[X₁X₂] is finite, then is an unbiased, consistent sequence of estimates of r.